# On the resolution requirements for modelling molecular gas formation in solar neighbourhood conditions

## TL;DR

This study determines the spatial resolution needed in simulations to accurately model molecular hydrogen and CO formation in the solar neighborhood, emphasizing the importance of resolving specific density and timescale conditions.

## Contribution

It provides critical resolution criteria and formulas to ensure convergence of molecular gas formation modeling in hydrodynamical simulations.

## Key findings

- H$_2$ converges at resolutions below 0.2 pc.
- CO requires resolutions below 0.04 pc for convergence.
- Derived conditions help verify molecule formation convergence in simulations.

## Abstract

The formation of molecular hydrogen (H$_2$) and carbon monoxide (CO) is sensitive to the volume and column density distribution of the turbulent interstellar medium. In this paper, we study H$_2$ and CO formation in a large set of hydrodynamical simulations of periodic boxes with driven supersonic turbulence, as well as in colliding flows with the \textsc{Flash} code. The simulations include a non-equilibrium chemistry network, gas self-gravity, and diffuse radiative transfer. We investigate the spatial resolution required to obtain a converged H$_2$ and CO mass fraction and formation history. From the numerical tests we find that H$_2$ converges at a spatial resolution of $\lesssim0.2$~pc, while the required resolution for CO convergence is $\lesssim 0.04$~pc in gas with solar metallicity which is subject to a solar neighbourhood interstellar radiation field. We derive two critical conditions from our numerical results: the simulation has to at least resolve the densities at which (1) the molecule formation time in each cell in the computational domain is equal to the dissociation time, and (2) the formation time is equal to the the typical cell crossing time. For both H$_2$ and CO, the second criterion is more restrictive. The formulae we derive can be used to check whether molecule formation is converged in any given simulation.